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  • The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style completeness theorem (degree of provability equals degree of truth) from which we get some particular cases by imposing restrictions on the formulas under consideration. As a particular case, we obtain completeness of fuzzy equational logic.
  • The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style completeness theorem (degree of provability equals degree of truth) from which we get some particular cases by imposing restrictions on the formulas under consideration. As a particular case, we obtain completeness of fuzzy equational logic. (en)
  • Výsledky studia Hornovy logiky. (cs)
Title
  • Fuzzy Horn logic I: proof theory
  • Fuzzy Horn logic I: proof theory (en)
  • Fuzzy Hornova logika I: důkaz teorie (cs)
skos:prefLabel
  • Fuzzy Horn logic I: proof theory
  • Fuzzy Horn logic I: proof theory (en)
  • Fuzzy Hornova logika I: důkaz teorie (cs)
skos:notation
  • RIV/61989592:15310/06:00002566!RIV07-AV0-15310___
http://linked.open.../vavai/riv/strany
  • 3-51
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(KJB1137301), Z(MSM6198959214)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
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http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 476577
http://linked.open...ai/riv/idVysledku
  • RIV/61989592:15310/06:00002566
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Fuzzy Horn logic; proof theory (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [C17A4F599B1C]
http://linked.open...i/riv/nazevZdroje
  • Archive for Mathematical Logic
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
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http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 45
http://linked.open...iv/tvurceVysledku
  • Bělohlávek, Radim
  • Vychodil, Vilém
http://linked.open...n/vavai/riv/zamer
issn
  • 0933-5846
number of pages
http://localhost/t...ganizacniJednotka
  • 15310
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